Extended warranty does not cover any electrical system or audio problems. Or so I understand. Certain electrically powered components such as the ECM, fuel pump, injectors, cruise control, starter motor, etc etc may be covered, but I don't know. Have not had a reason to find out...so far.
I am very sure that the battery is not covered under the ext warranty. I believe it is covered under the original new warranty...might be pro-rated as are most battery warrantys.